P-value functions are modern statistical tools that unify effect estimation and hypothesis testing and can provide alternative point and interval estimates compared to standard meta-analysis methods, using any of the many $p$-value combination procedures available (Xie et al., 2011, JASA). We provide a systematic comparison of different combination procedures, both from a theoretical perspective and through simulation. We show that many prominent p-value combination methods (e.g. Fisher's method) are not invariant to the orientation of the underlying one-sided p-values. Only Edgington's method, a lesser-known combination method based on the sum of $p$-values, is orientation-invariant and still provides confidence intervals not restricted to be symmetric around the point estimate. Adjustments for heterogeneity can also be made and results from a simulation study indicate that Edgington's method can compete with more standard meta-analytic methods.

翻译：p值函数是现代统计工具，它将效应估计与假设检验统一起来，并能提供与标准元分析方法不同的点估计和区间估计，可使用多种可用的$p$值组合程序（Xie等人，2011，JASA）。我们从理论角度和通过模拟，对不同组合程序进行了系统比较。我们发现许多著名的p值组合方法（例如Fisher方法）对基础单侧p值的方向不具有不变性。只有Edgington方法——一种基于$p$值之和的较不为人知的组合方法——具有方向不变性，并且仍能提供不限于点估计对称的置信区间。还可以进行异质性调整，模拟研究结果表明Edgington方法能够与更标准的元分析方法相竞争。